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arXiv · 1002.2856

On the gradient of Schwarz symmetrization of functions in Sobolev spaces

Marco Bramanti
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Abstract

Let S be a Sobolev or Orlicz-Sobolev space of functions not necessarily vanishing at the boundary of the domain. We give sufficient conditions on a nonnegative function in S in order that its spherical rearrangement ("Schwartz symmetrization") still belongs to S. These results are obtained via relative isoperimetric inequalities and somewhat generalize a well-known Polya-Szego's theorem. We also prove that the rearrangement of any function in S is locally in S.

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Marco Bramanti. 2010-02-15. On the gradient of Schwarz symmetrization of functions in Sobolev spaces. https://arxiv.org/abs/1002.2856

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